Congruent Triangles(3)




Problem

The angle XOY is less than 90 degrees.The point A is on the ray OX and the point P is on the ray OY.OABC and APDE are squares.
Prove that

(1) The triangle ABP and AOE are congruent.

(2) The segment BP and OE cross at right angle.

How to use this applet

1.Drag the red point to move the point A,P and X.
2.Click "Define this picture" button to fix the picture.
3.Click the radio button to choose the center point to rotate the triangle ABP.
4.Drag the red point to rotate the triangle ABP.
5.Click "Init" button to try again.